Free energy calculations using dual-level Born-Oppenheimer molecular dynamics

We describe an efficient and accurate method to compute free energy changes in complex chemical systems that cannot be described through classical molecular dynamics simulations, examples of which are chemical and photochemical reactions in solution, enzymes, interfaces, etc. It is based on the use of dual-level Born-Oppenheimer molecular dynamics simulations. A low-level quantum mechanical method is employed to calculate the potential of mean force through the umbrella sampling technique. Then, a high-level quantum mechanical method is used to estimate a free energy correction on selected points of the reaction coordinate using perturbation theory. The precision of the results is comparable to that of ab initio molecular dynamics methods such as the Car-Parrinello approach but the computational cost is much lower, roughly by two to three orders of magnitude. The method is illustrated by discussing the association free energy of simple organometallic compounds, although the field of application is very broad.